In 1938, at the age of twenty, Garayev composed his first musical piece, a cantata "The Song of the Heart" to the poem by Rasul Rza.

Garayev conducted his cantata during the Decade of Azerbaijani Art festival in the Bolshoi Theater, an event also attended by Stalin.

In the same year, Garayev moved to the Moscow State Conservatoire, where he became a student and a good friend of Dmitri Shostakovich.

In 1948, at the age of 30, Garayev was again awarded this prize for his symphonic poem Leyli and Majnun, based on the same-titled famous work of Nizami Ganjavi.

Based on Nizami Ganjavi's famous poem, Seven Beauties ("Yeddi gözəl") opened a new chapter in the history of classical music of Azerbaijan.

Garayev's only other ballet, Path of Thunder ("İldırımlı yollarla"), staged in 1958, was dedicated to racial conflicts in South Africa.

During his teaching career at the Azerbaijan State Conservatoire, Garayev tutored a number of prominent Azerbaijani musicians and composers, including Galib Mammadov, Arif Malikov, Khayyam Mirzazade and Ismayil Hajibeyov [az] among others.

Garayev's son, Faraj (born 1943), also became his student and went on to compose single-act ballets such as Shadows of Qobustan ("Qobustanın kölgələri") and Kaleidoscope, and later led the musical avant-garde movement in Azerbaijan.

During the Cold War in June 1961, Garayev and Tikhon Khrennikov were the only two Soviet composers who attended the first International Los Angeles Music Festival held at UCLA.

Garayev suffered from heart disease, which prevented him from attending his own 60th jubilee celebration held in Baku, where he was awarded the title of the Hero of Socialist Labor.

He made his students learn the inner workings of folk music.It seems like all civilization is in Garayev's hands, not as simple encyclopedic data but in a profound way.

That's why there were always so many people in Garayev's classes all the time despite how hard it was to enroll with him.The International Festival of Contemporary Music has been held since 1986 with the support of the Ministry of Culture of Azerbaijan.